LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 111 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
152.1.g.a	$1$	$0.076$	$\Q$	$\Q(\sqrt{-38}) $	None	$-1$	$1$	$0$	$-1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
152.1.g.b	$1$	$0.076$	$\Q$	$\Q(\sqrt{-38}) $	None	$1$	$-1$	$0$	$-1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
152.1.k.a	$2$	$0.076$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-2}) $	None	$-1$	$1$	$0$	$0$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
152.1.u.a	$6$	$0.076$	$\Q(\zeta_{18})$	$\Q(\sqrt{-2}) $	None	$0$	$-3$	$0$	$0$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
152.2.a.a	$1$	$1.214$	$\Q$	None	None	$0$	$-2$	$-1$	$-3$	$+$	$q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots$
152.2.a.b	$1$	$1.214$	$\Q$	None	None	$0$	$1$	$0$	$3$	$-$	$q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots$
152.2.a.c	$3$	$1.214$	3.3.961.1	None	None	$0$	$1$	$1$	$4$	$-$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
152.2.b.a	$2$	$1.214$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots$
152.2.b.b	$4$	$1.214$	$\Q(\sqrt{-3}, \sqrt{5})$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots$
152.2.b.c	$12$	$1.214$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$
152.2.c.a	$2$	$1.214$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$4$		$q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots$
152.2.c.b	$16$	$1.214$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$-8$		$q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
152.2.i.a	$2$	$1.214$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-3$	$0$		$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
152.2.i.b	$2$	$1.214$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$4$	$0$		$q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
152.2.i.c	$6$	$1.214$	6.0.2696112.1	None	None	$0$	$-1$	$-1$	$-4$		$q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
152.2.o.a	$4$	$1.214$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$0$	$-6$	$0$	$0$		$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
152.2.o.b	$4$	$1.214$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	None	$0$	$6$	$0$	$0$		$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
152.2.o.c	$28$	$1.214$		None	None	$-3$	$-6$	$0$	$0$
152.2.p.a	$36$	$1.214$		None	None	$-1$	$0$	$0$	$-8$
152.2.q.a	$6$	$1.214$	$\Q(\zeta_{18})$	None	None	$0$	$-6$	$6$	$3$		$q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots$
152.2.q.b	$6$	$1.214$	$\Q(\zeta_{18})$	None	None	$0$	$9$	$-6$	$6$		$q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots$
152.2.q.c	$18$	$1.214$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$-9$		$q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots$
152.2.t.a	$108$	$1.214$		None	None	$-6$	$0$	$0$	$-6$
152.2.v.a	$12$	$1.214$	12.0.$\cdots$.1	$\Q(\sqrt{-2}) $	None	$0$	$-6$	$0$	$0$		$q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots$
152.2.v.b	$96$	$1.214$		None	None	$-6$	$-6$	$0$	$0$
152.3.e.a	$2$	$4.142$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$14$	$22$		$q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots$
152.3.e.b	$8$	$4.142$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	None	$0$	$0$	$-14$	$-6$		$q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots$
152.3.f.a	$36$	$4.142$		None	None	$2$	$0$	$0$	$0$
152.3.g.a	$3$	$4.142$	3.3.4104.1	$\Q(\sqrt{-38}) $	None	$-6$	$0$	$0$	$0$		$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
152.3.g.b	$3$	$4.142$	3.3.4104.1	$\Q(\sqrt{-38}) $	None	$6$	$0$	$0$	$0$		$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
152.3.g.c	$32$	$4.142$		None	None	$0$	$0$	$0$	$-4$
152.3.k.a	$4$	$4.142$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	None	$4$	$-2$	$0$	$0$		$q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots$
152.3.k.b	$72$	$4.142$		None	None	$-5$	$0$	$0$	$0$
152.3.l.a	$76$	$4.142$		None	None	$-3$	$0$	$0$	$-8$
152.3.n.a	$20$	$4.142$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$-6$	$0$	$-16$		$q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots$
152.3.r.a	$60$	$4.142$		None	None	$0$	$6$	$0$	$0$
152.3.s.a	$228$	$4.142$		None	None	$-6$	$0$	$0$	$-6$
152.3.u.a	$12$	$4.142$	12.0.$\cdots$.1	$\Q(\sqrt{-2}) $	None	$0$	$6$	$0$	$0$		$q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
152.3.u.b	$216$	$4.142$		None	None	$-6$	$-18$	$0$	$0$
152.4.a.a	$2$	$8.968$	$\Q(\sqrt{57}) $	None	None	$0$	$-1$	$-5$	$-6$	$-$	$q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots$
152.4.a.b	$3$	$8.968$	3.3.3221.1	None	None	$0$	$-5$	$2$	$-35$	$-$	$q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots$
152.4.a.c	$3$	$8.968$	3.3.7057.1	None	None	$0$	$4$	$7$	$7$	$+$	$q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots$
152.4.a.d	$5$	$8.968$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	None	$0$	$2$	$0$	$22$	$+$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
152.4.b.a	$2$	$8.968$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots$
152.4.b.b	$56$	$8.968$		None	None	$0$	$0$	$0$	$0$
152.4.c.a	$54$	$8.968$		None	None	$2$	$0$	$0$	$28$
152.4.i.a	$14$	$8.968$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	None	$0$	$5$	$5$	$-28$		$q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots$
152.4.i.b	$16$	$8.968$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$-5$	$-8$		$q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
152.4.o.a	$4$	$8.968$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	None	$0$	$-30$	$0$	$0$		$q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$
152.4.o.b	$112$	$8.968$		None	None	$-3$	$24$	$0$	$0$

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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
152.1.g.a	\(1\)	\(0.076\)	\(\Q\)	\(\Q(\sqrt{-38}) \)	None	\(-1\)	\(1\)	\(0\)	\(-1\)		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b	\(1\)	\(0.076\)	\(\Q\)	\(\Q(\sqrt{-38}) \)	None	\(1\)	\(-1\)	\(0\)	\(-1\)		\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
152.1.k.a	\(2\)	\(0.076\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-2}) \)	None	\(-1\)	\(1\)	\(0\)	\(0\)		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
152.1.u.a	\(6\)	\(0.076\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(-3\)	\(0\)	\(0\)		\(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
152.2.a.a	\(1\)	\(1.214\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-1\)	\(-3\)	\(+\)	\(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b	\(1\)	\(1.214\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(3\)	\(-\)	\(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c	\(3\)	\(1.214\)	3.3.961.1	None	None	\(0\)	\(1\)	\(1\)	\(4\)	\(-\)	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
152.2.b.a	\(2\)	\(1.214\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots\)
152.2.b.b	\(4\)	\(1.214\)	\(\Q(\sqrt{-3}, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
152.2.b.c	\(12\)	\(1.214\)	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
152.2.c.a	\(2\)	\(1.214\)	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(4\)		\(q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots\)
152.2.c.b	\(16\)	\(1.214\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
152.2.i.a	\(2\)	\(1.214\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-3\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b	\(2\)	\(1.214\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(4\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c	\(6\)	\(1.214\)	6.0.2696112.1	None	None	\(0\)	\(-1\)	\(-1\)	\(-4\)		\(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.2.o.a	\(4\)	\(1.214\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(0\)	\(-6\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.b	\(4\)	\(1.214\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(6\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.c	\(28\)	\(1.214\)		None	None	\(-3\)	\(-6\)	\(0\)	\(0\)
152.2.p.a	\(36\)	\(1.214\)		None	None	\(-1\)	\(0\)	\(0\)	\(-8\)
152.2.q.a	\(6\)	\(1.214\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(-6\)	\(6\)	\(3\)		\(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b	\(6\)	\(1.214\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(9\)	\(-6\)	\(6\)		\(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c	\(18\)	\(1.214\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-9\)		\(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
152.2.t.a	\(108\)	\(1.214\)		None	None	\(-6\)	\(0\)	\(0\)	\(-6\)
152.2.v.a	\(12\)	\(1.214\)	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(-6\)	\(0\)	\(0\)		\(q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
152.2.v.b	\(96\)	\(1.214\)		None	None	\(-6\)	\(-6\)	\(0\)	\(0\)
152.3.e.a	\(2\)	\(4.142\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(14\)	\(22\)		\(q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots\)
152.3.e.b	\(8\)	\(4.142\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	None	\(0\)	\(0\)	\(-14\)	\(-6\)		\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
152.3.f.a	\(36\)	\(4.142\)		None	None	\(2\)	\(0\)	\(0\)	\(0\)
152.3.g.a	\(3\)	\(4.142\)	3.3.4104.1	\(\Q(\sqrt{-38}) \)	None	\(-6\)	\(0\)	\(0\)	\(0\)		\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.b	\(3\)	\(4.142\)	3.3.4104.1	\(\Q(\sqrt{-38}) \)	None	\(6\)	\(0\)	\(0\)	\(0\)		\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.c	\(32\)	\(4.142\)		None	None	\(0\)	\(0\)	\(0\)	\(-4\)
152.3.k.a	\(4\)	\(4.142\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	None	\(4\)	\(-2\)	\(0\)	\(0\)		\(q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots\)
152.3.k.b	\(72\)	\(4.142\)		None	None	\(-5\)	\(0\)	\(0\)	\(0\)
152.3.l.a	\(76\)	\(4.142\)		None	None	\(-3\)	\(0\)	\(0\)	\(-8\)
152.3.n.a	\(20\)	\(4.142\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(-6\)	\(0\)	\(-16\)		\(q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
152.3.r.a	\(60\)	\(4.142\)		None	None	\(0\)	\(6\)	\(0\)	\(0\)
152.3.s.a	\(228\)	\(4.142\)		None	None	\(-6\)	\(0\)	\(0\)	\(-6\)
152.3.u.a	\(12\)	\(4.142\)	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(6\)	\(0\)	\(0\)		\(q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
152.3.u.b	\(216\)	\(4.142\)		None	None	\(-6\)	\(-18\)	\(0\)	\(0\)
152.4.a.a	\(2\)	\(8.968\)	\(\Q(\sqrt{57}) \)	None	None	\(0\)	\(-1\)	\(-5\)	\(-6\)	\(-\)	\(q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots\)
152.4.a.b	\(3\)	\(8.968\)	3.3.3221.1	None	None	\(0\)	\(-5\)	\(2\)	\(-35\)	\(-\)	\(q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
152.4.a.c	\(3\)	\(8.968\)	3.3.7057.1	None	None	\(0\)	\(4\)	\(7\)	\(7\)	\(+\)	\(q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
152.4.a.d	\(5\)	\(8.968\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	None	\(0\)	\(2\)	\(0\)	\(22\)	\(+\)	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
152.4.b.a	\(2\)	\(8.968\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots\)
152.4.b.b	\(56\)	\(8.968\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
152.4.c.a	\(54\)	\(8.968\)		None	None	\(2\)	\(0\)	\(0\)	\(28\)
152.4.i.a	\(14\)	\(8.968\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	None	\(0\)	\(5\)	\(5\)	\(-28\)		\(q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
152.4.i.b	\(16\)	\(8.968\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(-5\)	\(-8\)		\(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.4.o.a	\(4\)	\(8.968\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(-30\)	\(0\)	\(0\)		\(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b	\(112\)	\(8.968\)		None	None	\(-3\)	\(24\)	\(0\)	\(0\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.